The second trail I hiked on Memorial Day was Fillmore Trail, also part of the Dripping Springs area. Filmore Trail, unlike Dripping Springs and La Cueva, doesn’t have a trailhead at the road; in order to get to it you have to either take La Cueva Trail or Crawford Trail first
Fillmore Trail goes behind La Cueva rocks and towards Fillmore Canyon, which is the site of an old mine. Most of the mine area is on privately-owned land, but you can still hike into the canyon itself, which is visible from the visiter’s center.
With Fillmore Canyon there’s no big payoff moment where you go “Ooo! Ahh!” at the end and the trail is uphill the whole way, but there are some good views of the west side of the Organ Mountains and it’s something you can cross off your list and say you’ve done.